Local SU(5) unification from the heterotic string

Abstract

We construct a 6D supergravity theory which emerges as intermediate step in the compactification of the heterotic string to the supersymmetric standard model in four dimensions. The theory has = 2 supersymmetry and a gravitational sector with one tensor and two hypermultiplets in addition to the supergravity multiplet. Compactification to four dimensions occurs on a T2/2 orbifold which has two inequivalent pairs of fixed points with unbroken SU5 and SU2 × SU4 symmetry, respectively. All gauge, gravitational and mixed anomalies are cancelled by the Green-Schwarz mechanism. The model has partial 6D gauge-Higgs unification. Two quark-lepton generations are localized at the SU5 branes, the third family is composed of split bulk hypermultiplets. The top Yukawa coupling is given by the 6D gauge coupling, all other Yukawa couplings are generated by higher-dimensional operators at the SU5 branes. The presence of the SU2 × SU4 brane breaks SU5 and generates split gauge and Higgs multiplets with = 1 supersymmetry in four dimensions. The third generation is obtained from two split -plets and two split 10-plets, which together have the quantum numbers of one -plet and one 10-plet. This avoids unsuccessful SU5 predictions for Yukawa couplings of ordinary 4D SU5 grand unified theories.